The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute . Write a sine model, y is equal to A sine b t plus k , for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when t is equal to 0 and that the windmill turns counterclockwise at a constant rate.

The blade’s length gives an amplitude of 10 feet, and its axis is 30 feet above the ground, so the vertical shift is 30. Two rotations per minute means one rotation takes 30 seconds, giving angular frequency b = 2π/30 = π/15 radians per second. At t = 0 the blade points right, so its height is at the axis level; as it turns counterclockwise, its height initially increases, matching a sine curve with no phase shift. The model is y = 10 sin((π/15)t) + 30, choice C.

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